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100+ Free PAA UCR/UNA Practice Questions

Prepare for the PAA — Prueba de Aptitud Académica UCR / UNA (Costa Rica) exam with instant access — no signup required.

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Key Facts: PAA UCR/UNA Exam

45

Official Questions

IIP-UCR Official Guide

110 min

Time Limit

IIP-UCR Official Guide

7,000 CRC

Registration Fee

Sistema Admisión Universitaria

200–800

Score Scale

IIP-UCR Scoring Guidelines

The PAA is Costa Rica's flagship university entrance exam for UCR and UNA, administered by the Instituto de Investigaciones Psicológicas (IIP-UCR). It features 45 four-option multiple-choice questions completed in 1 hour 50 minutes on paper without calculators, measuring general mathematical and verbal reasoning rather than subject content. There is no pass mark: UCR combines the PAA (50%) with secondary school grades (50%) into a Promedio de Admisión on a 200–800 scale, while UNA weights the PAA at 60%. The official examination is administered in Spanish; this bank provides an English-language MCQ study adaptation.

Sample PAA UCR/UNA Practice Questions

Try these sample questions to test your PAA UCR/UNA exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1A student spends 1/3 of their monthly scholarship on food and 1/4 of the remainder on books. If they have 120,000 Costa Rican Colones left, what is the total amount of the scholarship in Colones?
A.240,000
B.180,000
C.320,000
D.160,000
Explanation: Let S be the total scholarship. After spending 1/3 on food, the remainder is 1 - 1/3 = 2/3 of S. The student spends 1/4 of this remainder on books: (1/4) * (2/3)S = (1/6)S. The remaining portion of the scholarship is (2/3)S - (1/6)S = (4/6 - 1/6)S = (3/6)S = (1/2)S. We are given that (1/2)S = 120,000 Colones. Multiplying both sides by 2 gives S = 240,000 Colones.
2If 8 identical water pumps can drain a municipal reservoir in 15 hours, how many additional pumps of the same capacity are required to drain the same reservoir in 10 hours?
A.4 pumps
B.12 pumps
C.6 pumps
D.2 pumps
Explanation: The total work required to drain the reservoir is inversely proportional to the number of pumps. Total pump-hours = 8 pumps * 15 hours = 120 pump-hours. To drain the reservoir in 10 hours, the total number of pumps needed is 120 / 10 = 12 pumps. Since there are already 8 pumps operating, the number of additional pumps required is 12 - 8 = 4 pumps.
3Consider the sequence: 3, 7, 15, 31, 63, ... What is the 7th term of this sequence?
A.255
B.127
C.511
D.191
Explanation: Notice the rule for each term: each term is obtained by multiplying the previous term by 2 and adding 1 (a_n = 2 * a_{n-1} + 1), or equivalently a_n = 2^{n+1} - 1. Term 1 is 3 (2^2 - 1). Term 2 is 7 (2^3 - 1). Term 3 is 15 (2^4 - 1). Term 4 is 31 (2^5 - 1). Term 5 is 63 (2^6 - 1). The 6th term is 2 * 63 + 1 = 127 (2^7 - 1). The 7th term is 2 * 127 + 1 = 255 (2^8 - 1 = 256 - 1 = 255).
4In a class of 40 students, 24 study French, 18 study German, and 6 study neither language. How many students study both French and German?
A.8
B.12
C.6
D.10
Explanation: Since 6 students study neither language, the number of students studying at least one of the two languages is 40 - 6 = 34. By the principle of inclusion-exclusion: Total(French or German) = French + German - Both. Substituting the given values: 34 = 24 + 18 - Both, which simplifies to 34 = 42 - Both. Therefore, Both = 42 - 34 = 8 students.
5A rectangle has a perimeter of 56 cm. If its length is 4 cm greater than three times its width, what is the area of the rectangle in square centimeters?
A.132
B.144
C.120
D.160
Explanation: Let w be the width and L be the length. The perimeter is 2(L + w) = 56, so L + w = 28. We are given L = 3w + 4. Substitute L into the sum: (3w + 4) + w = 28, which gives 4w + 4 = 28, so 4w = 24 and w = 6 cm. Then length L = 3(6) + 4 = 18 + 4 = 22 cm. Check perimeter: 2(22 + 6) = 2(28) = 56 cm. The area is L * w = 22 * 6 = 132 cm^2.
6The average (arithmetic mean) of five distinct positive integers is 20. If the median of these five numbers is 18, what is the greatest possible value that any one of the five integers could take?
A.59
B.62
C.55
D.64
Explanation: Let the five distinct integers sorted in ascending order be a < b < c < d < e. The sum of the five integers is 5 * 20 = 100. The median is the third number, so c = 18. To maximize the largest integer e, we must minimize the other four integers: a, b, and d. Since all numbers are distinct positive integers: the minimum possible value for a is 1; the minimum possible value for b is 2. The median is c = 18. The integer d must be strictly greater than c = 18, so the minimum integer value for d is 19. Now sum the four smallest possible values: a + b + c + d = 1 + 2 + 18 + 19 = 40. Therefore, the maximum possible value for e is 100 - 40 = 59.
7A merchant purchases a shipment of goods for 500,000 Colones. She sells 60% of the goods at a 25% profit over their purchase cost, and the remaining 40% of the goods at a 10% loss relative to their purchase cost. What is her net profit on the entire shipment in Colones?
A.55,000
B.75,000
C.60,000
D.45,000
Explanation: Cost of the first portion (60%): 0.60 * 500,000 = 300,000 Colones. Profit on this portion at 25%: 0.25 * 300,000 = +75,000 Colones. Cost of the remaining portion (40%): 0.40 * 500,000 = 200,000 Colones. Loss on this portion at 10%: 0.10 * 200,000 = -20,000 Colones. Net profit = Profit on first part - Loss on second part = 75,000 - 20,000 = 55,000 Colones.
8Two cyclists, Alejandro and Beatriz, start at the same time from points 90 kilometers apart and travel toward each other on a straight road. Alejandro rides at a constant speed of 18 km/h and Beatriz rides at a constant speed of 12 km/h. How many kilometers will Alejandro have traveled when they meet?
A.54 km
B.36 km
C.45 km
D.60 km
Explanation: Since they travel toward each other, their relative speed of convergence is the sum of their individual speeds: 18 km/h + 12 km/h = 30 km/h. The time required for them to meet is Distance / Relative Speed = 90 km / 30 km/h = 3 hours. In 3 hours, Alejandro travels: Distance = Speed * Time = 18 km/h * 3 h = 54 km.
9If x and y are positive integers such that x^2 - y^2 = 45 and x - y = 3, what is the value of the product x * y?
A.54
B.48
C.60
D.36
Explanation: Factor the difference of squares: (x - y)(x + y) = 45. Given x - y = 3, substitute into the equation: 3 * (x + y) = 45, which gives x + y = 15. Now solve the linear system: x - y = 3 and x + y = 15. Adding the two equations: 2x = 18 => x = 9. Subtracting the first equation from the second: 2y = 12 => y = 6. Both x = 9 and y = 6 are positive integers. The product x * y = 9 * 6 = 54.
10A container has a mixture of 60 liters of milk and water, where 20% of the mixture is water. How many liters of pure water must be added to make water constitute 40% of the new mixture?
A.20 liters
B.15 liters
C.24 liters
D.12 liters
Explanation: Initially, the container has 60 liters. Water is 20% of 60 = 12 liters. The amount of pure milk is 60 - 12 = 48 liters. When pure water is added, the quantity of milk remains unchanged at 48 liters. In the new mixture, water is 40%, which means milk must constitute 60% of the new mixture. Let T be the total volume of the new mixture. Then 0.60 * T = 48 liters, so T = 48 / 0.60 = 80 liters. The amount of water added is the increase in total volume: 80 - 60 = 20 liters.

About the PAA UCR/UNA Exam

The Prueba de Aptitud Académica (PAA) is the standardized university entrance examination for the Universidad de Costa Rica (UCR) and Universidad Nacional (UNA), measuring general mathematical and verbal reasoning.

Assessment

45 four-option multiple-choice items administered in a single 110-minute session

Time Limit

110 minutes

Passing Score

No pass mark; applicants who obtain a Promedio de Admisión (200–800 scale) are elegible and compete for places against per-career cut scores

Exam Fee

7,000 CRC (Instituto de Investigaciones Psicológicas (IIP-UCR))

PAA UCR/UNA Exam Content Outline

Split not published

Mathematical Reasoning (Razonamiento Matemático)

Arithmetic problem solving, algebra, proportional reasoning, geometry, number patterns, and deductive logic. IIP-UCR publishes the 45-item total but not a fixed verbal/mathematical item split.

Split not published

Verbal Reasoning (Razonamiento Verbal)

Reading comprehension, textual analysis, contextual vocabulary, semantic relationships, presuppositions, and inferential logic. This practice bank divides its 100 items evenly between the two reasoning areas.

How to Pass the PAA UCR/UNA Exam

What You Need to Know

  • Passing score: No pass mark; applicants who obtain a Promedio de Admisión (200–800 scale) are elegible and compete for places against per-career cut scores
  • Assessment: 45 four-option multiple-choice items administered in a single 110-minute session
  • Time limit: 110 minutes
  • Exam fee: 7,000 CRC

Keys to Passing

  • Work through all 100 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

PAA UCR/UNA Study Tips from Top Performers

1Allocate an average of 2 minutes per question to comfortably finish within the 110-minute testing window.
2Practice mental arithmetic and fraction manipulation to solve quantitative reasoning items swiftly without a calculator.
3For verbal items, identify the primary logical assertion before reviewing the options to avoid falling for tempting partial-truth distractors.
4Review basic Euclidean geometry formulas for perimeter, area, volume, and the Pythagorean theorem.

Frequently Asked Questions

What is the structure of the official PAA?

The official PAA administered by IIP-UCR contains 45 multiple-choice questions with four options each. Candidates have 1 hour and 50 minutes (110 minutes) to complete the test on an optical answer sheet without calculators.

How is the admission score calculated for UCR and UNA?

At UCR, the admission score (Promedio de Admisión) is composed of 50% from the PAA score and 50% from the secondary school GPA (penultimate year core subjects). At UNA, the PAA weights 60% and secondary school grades weight 40%.

Is there a minimum score needed to pass the PAA?

No. IIP-UCR states plainly that the PAA has no pass mark. UCR's Consejo Universitario removed the old 442-point eligibility minimum in 2020, so every applicant who obtains a Promedio de Admisión is elegible and may compete for two careers; places are then awarded in rank order against each career's own cut score. UNA publishes no cut score at all.

Can calculators be used during the PAA?

No. The use of electronic devices, calculators, smartwatches, and phones is strictly prohibited during the PAA. All mathematical reasoning items are designed to be solved through arithmetic and logical deduction by hand.

Is this practice bank in Spanish like the real exam?

No. The official exam is administered entirely in Spanish by the IIP-UCR. This practice bank provides an English-language MCQ study adaptation of the mathematical and verbal reasoning skills measured on the PAA for English-speaking candidates and international students.